Definitions

A pinnacle point is a point from which no higher point can be seen.

More specifically, a pinnacle point is a point with zero inferiority, where inferiority is defined as the maximum elevation that can be seen in a direct line of sight from a point minus the point's elevation. Since all points can see themselves, the minimum possible inferiority is zero.

Finding Pinnacle Points

Thanks to Kai Xu for inspiring my search for pinnacle points with his own search for on-top-of-the-world mountains. Also, thanks to Andrew Kirmse for his list of 11,866,713 summits with a prominence greater than 100 ft. I would not have been able to get this project off the ground without it. Even with it, I have to make many approximations. I assume the Earth to be a sphere instead of an oblate spheroid, and I do not take the effect of atmospheric refraction into account.

For all 11,866,713 summits, I find the summit's horizon distance defined as √(2*R_earth*Prominence). Prominence is used instead of elevation since prominence is a better measure of a summit's rise above its surroundings. I use an algorithm to find all summits that have no higher summits in view. I define two summits to be in view if their geospatial distance is less than the sum of their horizon distances. This is far from ideal. Not only is the equation for horizon distance an approximation, the very concept of horizon distance is flawed. Ultimately, viewshed analysis needs to be done to find Earth's pinnacle points with greater confidence and accuracy. I am investigating how to best do this given the high computational cost of viewshed analysis.

Check out the latest on my github. Contact me at jamiegbreault@gmail.com.